Cartoon of phase conditions for Bragg’s law
Matlab code 

% Program to generate a cartoon of Bragg's law

 

clear; close all;

 

figure('units','pixels','position',[0 0 1920 1080],'ToolBar','none');

vid = VideoWriter('braggsLaw1.mp4','MPEG-4');

vid.Quality = 100;

vid.FrameRate = 30;

open(vid);

set(0,'defaultfigurecolor',[1 1 1]);

set(gca,'linewidth',7);

set(gca, 'Projection','perspective');

lp1 = [-0.4 -10.7 1.4];

lp2 = [0.4 -0. 1.4];

myBlue = [0.3 0.34 0.61];

myGold = [0.7 0.6 0];

myPurple = [0.5 0 0.5];

axis equal

 

LL = 4;

d = 1;

lambda = 0.5;

 

xlim([-LL LL]);

ylim([-LL LL]);

zlim([-LL LL]);

 

 

[x,y,z] = sphere(40); % Create sphere coordinates

ar = 0.25; % radius of atoms

 

thetaStart = 20;

thetaEnd = 40;

thetaStep = 0.1;

nthsteps = (thetaEnd-thetaStart)/thetaStep;

 

fwd = [thetaStart:thetaStep:thetaEnd];

 

for theta = [fwd flip(fwd)] % from min angle to max and back again 

    hold off

    for jj = 0:3

        for ii=-3:3

            atom = surf(ii*d+x*ar,y*ar,z*ar-jj*d,'FaceAlpha',(4.7-jj)/5,'FaceColor',myBlue, ...

                'LineStyle','none','FaceLighting','gouraud','DiffuseStrength',1, ...

                'AmbientStrength',0.1);

            hold on

        end

        set(gca, 'Projection','perspective');

        set(gca,'View',[0,0]);

        axis equal

        xlim([-LL LL]);

        ylim([-LL LL]);

        zlim([-LL LL]);

 

        % incident x-rays at angle theta to atomic planes

        rayLength = 2*LL+jj*d*sind(theta);

        braggAng = asind(2*lambda/(2*d));

        offdiff = abs((braggAng-theta)/braggAng);

        if (offdiff <= 0.01)

            myCol = [1 0 0];

            myCol2 = myCol;

        else

            myCol = myGold;

            myCol2 = [0 0 0];

        end

        wavex = 0:LL/200:rayLength;

        wavey = 0.0*wavex-0.25;

        wavez = 0.2*sin(2*pi*(wavex/lambda))-jj;

        h = plot3(wavex-rayLength,wavey,wavez,'color',myCol, 'LineWidth', 3.5);

        rotate(h,[0 1 0],theta,[0,-0.25,-jj]);

        h.Color(4) = (4.7-jj)/5; % Semitransparent line

 

        % x-rays scattered by 2theta

        wavex = 0:LL/200:2*LL+jj*sind(theta);

        wavez = 0.2*sin(2*pi*(wavex+jj*d*sind(theta))/lambda);

        h = plot3(wavex,wavey,wavez-jj*d,'color',myCol, 'LineWidth', 3.5);

        rotate(h,[0 1 0],-theta,[0,-0.25,-d*jj]);

        h.Color(4) = (4-jj)/5; % Semitransparent line

 

        % Peak-indicating dot-dashed lines showing phase differences

        phline = plot3([2-3*lambda/4-jj*d*(sind(theta)-1) ...

            2-3*lambda/4-jj*d*(sind(theta)-1)],[-0.25 -0.25], ...

            [0.5-d*jj -0.5-d*jj],'color',myCol2, 'LineWidth',1.4,'LineStyle','-.');

        rotate(phline,[0 1 0],-theta,[0,-0.25,-d*jj]);

 

        % Plot Gaussian to represent Bragg peak signal

        gaussx = [-0.5:1/nthsteps:0.5];

        gaussy = 0*gaussx;

        gaussz = 1+exp(-gaussx.^2/0.01);

        gaIndex = (theta-thetaStart)/thetaStep+1;

        gauss = plot3(gaussx(1:gaIndex),gaussy(1:gaIndex),gaussz(1:gaIndex), ...

            'color',myCol2,'LineWidth',2);

        hText = text(0, 0, 0.83,'2\theta', 'FontSize',18,'HorizontalAlignment', 'center');

 

 

        % In and out arrows

        arrow1 = mArrow3([-LL -0.4 -1.5*d],[-LL+1 -0.4 -1.5*d],'color',myGold, ...

            'stemWidth',0.05,'tipWidth',0.1,'facealpha',1); %

        rotate(arrow1,[0 1 0],theta,[0,-0.4,-1.5*d]);

        arrow2 = mArrow3([LL-1 -0.4 -1.5*d],[LL -0.4 -1.5*d],'color',myGold, ...

            'stemWidth',0.05,'tipWidth',0.1,'facealpha',1); %

        rotate(arrow2,[0 1 0],-theta,[0,-0.4,-1.5*d]);

 

    end

    light('Position',lp1,'Style','infinite');

    light('Position',lp2,'Style','infinite');

 

    axis off

    frame = getframe(gcf);

    writeVideo(vid,frame);

 

end

 

% Output the movie as an mpg file

close(vid);